/explore
|
You are here 
|
ckrao.wordpress.com | ||
| | | | |
mikespivey.wordpress.com
It's fairly well-known, to those who know it, that $latex \displaystyle \left(\sum_{k=1}^n k \right)^2 = \frac{n^2(n+1)^2}{4} = \sum_{k=1}^n k^3 $. In other words, the square of the sum of the first n positive integers equals the sum of the cubes of the first n positive integers. It's probably less well-known that a similar relationship holds... |
|
| | | | | ||
| | | | |
algorithmsoup.wordpress.com
The ``probabilistic method'' is the art of applying probabilistic thinking to non-probabilistic problems. Applications of the probabilistic method often feel like magic. Here is my favorite example: Theorem (Erdös, 1965). Call a set $latex {X}&fg=000000$ sum-free if for all $latex {a, b \in X}&fg=000000$, we have $latex {a + b \not\in X}&fg=000000$. For any finite... |
|
| | | | | ||
| | | | |
thatsmaths.com
We are all familiar with Pascal's Triangle, also known as the Arithmetic Triangle (AT). Each entry in the AT is the sum of the two closest entries in the row above it. The $latex {k}&fg=000000$-th entry in row $latex {n}&fg=000000$ is the binomial coefficient $latex {\binom{n}{k}}&fg=000000$ (read $latex {n}&fg=000000$-choose-$latex {k}&fg=000000$), the number of ways of... |
|
| | | | | ||
| | | | |
www.chrisstucchio.com
On a number of occasions, I've spoken to prospective clients and observed others making the following mistake. They've set up an A/B test or bandit system using relatively standard statistical methodology. Unfortunately, their sample size is prohibitively low. In order to |
|
| | | |||
